Darbo type $ \mathcal{Z}_{\rm{m}} $-contraction and Darbo type $ \mathcal{L}_{\rm{m}} $-contraction are introduced and some fixed point results are established for such contraction mappings. As an application, we prove the existence of solution of a Caputo fractional Volterra-Fredholm integro-differential equation via integral type boundary conditions and verify the validity of our application by an appropriate example.
Citation: Mian Bahadur Zada, Muhammad Sarwar, Reny George, Zoran D. Mitrović. Darbo-Type $ \mathcal{Z}_{\rm{m}} $ and $ \mathcal{L}_{\rm{m}} $ contractions and its applications to Caputo fractional integro-differential equations[J]. AIMS Mathematics, 2021, 6(6): 6340-6355. doi: 10.3934/math.2021372
Darbo type $ \mathcal{Z}_{\rm{m}} $-contraction and Darbo type $ \mathcal{L}_{\rm{m}} $-contraction are introduced and some fixed point results are established for such contraction mappings. As an application, we prove the existence of solution of a Caputo fractional Volterra-Fredholm integro-differential equation via integral type boundary conditions and verify the validity of our application by an appropriate example.
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Mian Bahadur Zada, Muhammad Sarwar, Reny George, Zoran D. Mitrović. Darbo-Type $ \mathcal{Z}_{\rm{m}} $ and $ \mathcal{L}_{\rm{m}} $ contractions and its applications to Caputo fractional integro-differential equations[J]. AIMS Mathematics, 2021, 6(6): 6340-6355. doi: 10.3934/math.2021372
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